11 November 2013 09:23:18 AM
DIFFER_PRB:
C++ version
Test the DIFFER library.
TEST01
Demonstrate that the DIFFER matrix is 'really'
a Vandermonde matrix.
Stencil matrix:
Col: 0 1 2 3
Row
0: 2.5 3.3 -1.3 0.5
1: 6.25 10.89 1.69 0.25
2: 15.625 35.937 -2.197 0.125
3: 39.0625 118.592 2.8561 0.0625
Solution of DIFFER system:
0: 1
1: 2
2: 3
3: 4
Solution of VANDERMONDE system:
0: 2.5
1: 6.6
2: -3.9
3: 2
Transformed solution of VANDERMONDE system:
0: 1
1: 2
2: 3
3: 4
TEST02
DIFFER_INVERSE returns the inverse of a DIFFER matrix;
N Inverse error
2 0
2 4.44089e-16
2 8.88185e-16
2 4.44089e-16
2 0
3 1.17776e-14
3 1.65635e-13
3 2.87917e-15
3 5.12266e-14
3 1.8897e-14
4 3.14213e-14
4 8.5015e-14
4 5.71398e-14
4 4.28707e-14
4 2.80585e-12
5 1.43579e-10
5 1.45624e-12
5 1.81003e-11
5 2.30649e-12
5 1.19425e-11
6 8.31044e-10
6 8.46168e-11
6 7.55719e-12
6 7.24273e-12
6 1.81026e-11
7 4.73678e-10
7 5.59992e-11
7 5.32315e-10
7 2.01382e-11
7 3.07994e-11
8 5.89396e-10
8 5.9282e-10
8 9.3962e-09
8 1.04455e-09
8 1.7787e-09
TEST03
Reproduce a specific example.
Solution of DIFFER system:
0: -0.0833333
1: 0.5
2: -1.5
3: 0.25
DFDX = 3.66931
d exp(x) /dx = 3.6693
TEST04
DIFFER_FORWARD,
DIFFER_BACKWARD, and
DIFFER_CENTRAL produce coefficients for difference
approximations of the O-th derivative,
with error of order H^P, for a uniform spacing of H.
Use a spacing of H = 1 for all examples.
Forward difference coefficients, O = 3, P = 1
0: 0 -1
1: 1 3
2: 2 -3
3: 3 1
Backward difference coefficients, O = 3, P = 1
0: -3 -1
1: -2 3
2: -1 -3
3: 0 1
Central difference coefficients, O = 3, P = 2
0: -2 -0.5
1: -1 1
2: 0 0
3: 1 -1
4: 2 0.5
Central difference coefficients, O = 3, P = 4
0: -3 0.125
1: -2 -1
2: -1 1.625
3: 0 0
4: 1 -1.625
5: 2 1
6: 3 -0.125
Forward difference coefficients, O = 4, P = 1
0: 0 1
1: 1 -4
2: 2 6
3: 3 -4
4: 4 1
Backward difference coefficients, O = 4, P = 1
0: -4 1
1: -3 -4
2: -2 6
3: -1 -4
4: 0 1
Central difference coefficients, O = 4, P = 3
0: -3 -0.166667
1: -2 2
2: -1 -6.5
3: 0 9.33333
4: 1 -6.5
5: 2 2
6: 3 -0.166667
TEST05
DIFFER_STENCIL produces coefficients for difference
approximations of the O-th derivative,
using arbitrarily spaced data, with maximum spacing H
with error of order H^P.
Use a spacing of H = 1 for all examples.
Forward difference coefficients, O = 3, P = 1
0: 0 -1
1: 1 3
2: 2 -3
3: 3 1
Backward difference coefficients, O = 3, P = 1
0: -3 -1
1: -2 3
2: -1 -3
3: 0 1
Central difference coefficients, O = 3, P = 2
0: -2 -0.5
1: -1 1
2: 0 0
3: 1 -1
4: 2 0.5
Central difference coefficients, O = 3, P = 4
0: -3 0.125
1: -2 -1
2: -1 1.625
3: 0 0
4: 1 -1.625
5: 2 1
6: 3 -0.125
Forward difference coefficients, O = 4, P = 1
0: 0 1
1: 1 -4
2: 2 6
3: 3 -4
4: 4 1
Backward difference coefficients, O = 4, P = 1
0: -4 1
1: -3 -4
2: -2 6
3: -1 -4
4: 0 1
Central difference coefficients, O = 4, P = 3
0: -3 -0.166667
1: -2 2
2: -1 -6.5
3: 0 9.33333
4: 1 -6.5
5: 2 2
6: 3 -0.166667
DIFFER_PRB:
Normal end of execution.
11 November 2013 09:23:18 AM